NEUTRON NOISE CALCULATION IN A
LARGE SFR CORE AND ANALYSIS OF
ITS PROPERTIES
Florian Zylbersztejn
CEA, DEN, Cadarache, DER/SPEx/LDCI
Christian Jammes, Philippe Filliatre.
CEA, DEN, Cadarache, DER/SPEx/LDCI
Imre Pazsit, Hoai Nam Tran, Paolo Vinai, Christophe Demazière.
SOMMAIRE
TABLE OF CONTENTS:
Introduction & ESFR core
1) Reminder of the Neutron noise equations
2) Verification of the CORESIM code
2) Verification of the CORESIM code
3) Neutron noise calculations: results and analysis
INTRODUCTION
Context:
Renewal of the fast reactors field with the Generation-IV international forum. Project of industrial prototype (Astrid) by the CEA in France.
The next generation of SFR must have improved safety requirements on every topics.
every topics.
Neutron noise simulation:
Not explored enough for fast systems.
Enhance neutron diagnosis to improve the safety.
1) REMINDER OF THE NEUTRON NOISE EQUATIONS
General operator form of diffusion equation :
Static flux calculation: eigen-values problem
Noise equations : source problem in complex formalism
S
P
k
B
dt
d
v
+
φ
=
effφ
+
1
)
(
1
Similar equations: same solving algorithm.
Results of neutron noise: good as long as static flux calculations are good
( )
( ) ( )
( )
( )
( )
( )
2 , , ' ' , ' ' ' ' 1 , , , , , g g t g g g f g g s g g g g g g g eff g D r r r r S r k δφ ω ω δφ ω χ ω ν δφ ω → δφ ω ω ≠ ≠ − ∇ +∑ =∑
∑ +∑
∑ +( )
,( ) ( )
, '( ) ( )
'( )
, '( ) ( )
' ' ' 1 , t g g s g g g g f g g g g eff g g r r r S r k δ ω φ δ ω φ χ ω δν ω φ ω → ≠ =− ∑ +∑
∑ +∑
∑MAIN FEATURES OF CORESIM
Some characteristics:Solving diffusion equations for static and dynamic states(i.e. noise in frequency domain). 3-D, multi-energy groups, multi-groups of delayed precursors.
Finite differences for spatial discretization.
Power iterative solution for both static and noise solutions. CMFD acceleration for both static and noise calculations. Language: Matlab scripts.
GENERAL LAYOUT OF THE ESFR CORE
Model chosen for this study: ESFR core
Optimized large fast neutron reactor.
2) VERIFICATION OF THE CORESIM CODE
Results of static calculations:Comparison with ERANOS: CEA code suite widely validated from integral measurements.
Conditions of calculations:
Same core model (macro XS)
ERANOS: Transport / CORESIM: diffusion
Eigenvalue ERANOS Noise simulator
NEUTRON FLUX SPATIAL DISTRIBUTION
Fast groups
COMPARISON OF POWER DISTRIBUTION
# ERANOS results # Relative error (%)
3) NEUTRON NOISE CALCULATIONS: RESULTS AND ANALYSIS
Scenario of perturbation: boiling
Cross section perturbation: generated with ERANOS Realistic frequency content: white noise [0.1Hz-10Hz] Neutron noise source: Each kind of cross section
NEUTRON NOISE EVALUATION FROM BOILING SOURCE
Results of Neutron noise:
Spatial dependence of the amplitude.
Frequency dependence. Evolution of the phase. Source position
Fuel C1
Fuel C2
NOISE AT LOW FREQUENCY: DEVIATION FROM POINT KINETIC
NOISE AT HIGHER FREQUENCIES
Frequency = 1.0 Hz
RADIAL NEUTRON NOISE EVOLUTION
Fast group
ANALYSIS OF THE RESULTS OF CALCULATIONS
CORESIM system code: provide and the phase.
The 33 group energy-dependant noise: interesting for the understanding of
the physical processes.
• f 0 Hz : Shape of the neutron noise shape Static flux shape. • f ∞ : Shape of the neutron noise shape Only a localized
component.
)
,
(
r
r
E
Φ
δ
To compute the ‘’measurable’’ neutron noise : integration over a detector XS.
Provide the measurable localized components of the neutron noise.
Cross section perturbations: realistic model, for energy dependence & amplitude.
The relative noise : correct order of magnitude of noise measurement.
Φ
Φ
‘’MEASURABLE’’ NEUTRON NOISE:
SPATIAL DEPENDENCESource location
: first assembly ringSmall amplitude:
10% boilingRELATIVE ‘’MEASURABLE’’ NEUTRON NOISE: SPATIAL DEPENDENCE
The deviation from static flux shape become more visible.
‘’MEASURABLE’’ NEUTRON NOISE:
SPATIAL DEPENDENCEAnother location
: at power peakHigher amplitude
: 50% boilingRELATIVE ‘’MEASURABLE’’ NEUTRON NOISE: SPATIAL DEPENDENCE
The deviation from static flux shape become visible.
CONCLUSIONS
The new CORESIM system code:
Solving algorithm: Verified with the reliable Ecco-Eranos code.
Solve the neutron noise equations: 1rs order perturbations & diffusion.
Estimation of the
δΦ
(r,E,
ω
) neutron noise:
Any scenario of oscillating perturbations.
33 group energy meshing: better understanding. 33 group energy meshing:
Applications for neutron diagnostics.
Conclusion on sodium boiling results:
Appearance of a localized component in the core. Noise level at detection location can be calculated. No localization possible from out core monitoring
TITRE DE LA DIAPOSITIVE
Sous-titre
Sandipis cilismo dionseq uiscili smodiamet, secte doloreet,vulputem volore modionsed tat :
equisnumipit alis nos exerosalis amcore feuguevercillamet aliquis dolessit veliquat lut ver ipsusciliquat. Amvelessequis adiamiriusciniam, velisat.
Docommy nullaor eratuersimvent wis non enibh esto odolor sent loreet incipsum vent at, consequatametue feu facitatummynibh exer sumvel ut la consequatue dipit
aliquamet lumsan eui blam et iriure feugiatpraesse quipis nosnos nulluptating eumvelenimquat wisdelestrud tateet adipea feu
facillaore tin vel do od dolorperilit prat diatum ing ea acilit am alit - sed tet, sissendiam eum zzrit
- quatinisim eraestrud min hendipitnibh
TITRE DE LA DIAPOSITIVE
Sous-titre
Sandipis cilismo dionseq uiscili
smodiamet, secte doloreet,vulputem volore modionsed tat.
Amcore feuguevercillamet aliquis dolessit veliquat lut ver ipsusciliquat. Amvelessequis adiamiriusciniam, velisat.
Docommy nullaor eratuersimvent wis non enibh esto odolor sent loreet incipsum vent at, consequatametue feu facitatummynibh exer sumvel ut la consequatue. Esto odolor sent loreet ecte doloreet,vulputem volore modionsed tat.
Direction de l’Energie Nucléaire Département d’Etudes des Réacteurs
Commissariat à l’énergie atomique et aux énergies alternatives Centre de Cadarache| 13108 Saint-Paul-les-Durance Cedex | PAGE 28
